Constructing random matrices to represent real ecosystems

Alex James*, Michael J. Plank, Axel G. Rossberg, Jonathan Beecham, Mark Emmerson, Jonathan W. Pitchford

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


Models of complex systems with n components typically have order n<sup>2</sup> parameters because each component can potentially interact with every other. When it is impractical to measure these parameters, one may choose random parameter values and study the emergent statistical properties at the system level. Many influential results in theoretical ecology have been derived from two key assumptions: that species interact with random partners at random intensities and that intraspecific competition is comparable between species. Under these assumptions, community dynamics can be described by a community matrix that is often amenable to mathematical analysis. We combine empirical data with mathematical theory to show that both of these assumptions lead to results that must be interpreted with caution. We examine 21 empirically derived community matrices constructed using three established, independent methods. The empirically derived systems are more stable by orders of magnitude than results from random matrices. This consistent disparity is not explained by existing results on predator-prey interactions. We investigate the key properties of empirical community matrices that distinguish them from random matrices. We show that network topology is less important than the relationship between a species’ trophic position within the food web and its interaction strengths. We identify key features of empirical networks that must be preserved if random matrix models are to capture the features of real ecosystems.

Original languageEnglish
Pages (from-to)680-692
Number of pages13
JournalAmerican Naturalist
Issue number5
Early online date11 Mar 2015
Publication statusPublished - May 2015


  • Community matrix
  • Complexity
  • Food web
  • Interaction strength
  • Predator-prey interaction
  • Stability

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics


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